How can I create this type of lighting effect in Blender Cycles?
There are two main differences I see between your render and the reference image: the shader and the lighting.



Shading

It looks like in your render you have only used a glossy shader with a red color for the cubes.  However in the real world, the glossy reflections are rarely colored (except on metallics), the color comes from the diffusion.  See how the glossy reflections on the reference image are actually white (the color of the light and background), not red?

Here is my node setup for a general plastic material.



The base is just a diffuse with a little bit of SSS and gloss, then a sharp Fresnel gloss mixed in.



Lighting

There are 3 main differences I noticed about the lighting in your reference image versus your render.


The white backdrop.  To make a white backdrop like what is shown, create a plane, extrude the back edge up, add a subsurf modifier, and add some proximity cuts near the corner to hold the curve to the corner.  Just use a pure white diffuse shader for its material.





The shadows are very soft.  To create soft shadows in Cycles you need to use larger values for the Size parameter on your lamps (found under the Lamp rollout of the Object Data properties panel).  This effectively blurs the edges of shadows produced by that lamp.





The shadows are directly underneath the object.  To create shadows like this I like to use several sun lamps aimed in slightly different directions with different shadow sizes and strengths.  I usually have one slightly brighter main light, and two dimmer backup lights with even larger shadow sizes aimed in opposite directions and angles from the main light.






Result

Here's my result: